Wien’s Displacement Calculator
About the Wien’s Displacement Calculator
The Wien’s Displacement Calculator is a scientifically precise, real-time online tool that computes the peak wavelength (λ_max) of blackbody radiation using Wien’s displacement law λ_max × T = b, where b = 2897.771955 µm·K (CODATA 2018 value). It also calculates the corresponding peak frequency, spectral radiance at the peak, and the dominant electromagnetic band (UV, visible, IR) for any temperature. Based on Max Wien’s 1893 derivation from classical thermodynamics and validated by Planck’s quantum law, this calculator delivers publication-grade results trusted by physicists, astronomers, engineers, and researchers studying thermal radiation, remote sensing, and climate.
Learn more about the law and its derivation at Wien’s Displacement on Wikipedia.
Importance of the Wien’s Displacement Calculator
Wien’s displacement law reveals how the spectral peak of thermal emission shifts with temperature: hotter objects emit at shorter wavelengths. The Sun (≈5800 K) peaks in visible green light, Earth (≈288 K) in long-wave infrared (~10 µm), and industrial furnaces (>1000 K) in near-IR. This principle underpins color temperature in photography, pyrometry for non-contact temperature measurement, thermal imaging, and satellite remote sensing of land surface temperature (LST). In agriculture, LST derived from thermal IR bands (using Wien’s law for band selection) monitors crop water stress, soil moisture, frost risk, and disease outbreaks. Accurate peak wavelength calculation ensures correct sensor band choice and calibration, improving yield prediction and irrigation efficiency — sustainable practices promoted by Agri Care Hub.
Purpose of the Wien’s Displacement Calculator
Key calculations:
- Peak wavelength λ_max = b / T with b = 2897.771955 µm·K
- Peak frequency ν_max ≈ 5.879 × 10^10 × T Hz
- Dominant spectral band (UV, visible, NIR, MIR, FIR)
- Color temperature perception for visible range
- Comparison to real objects (stars, human body, soil, vegetation)
When and Why You Should Use It
Use this tool when you need to:
- Select optimal thermal IR band for satellite LST retrieval
- Calibrate pyrometers or thermal cameras
- Estimate crop canopy temperature from emission peak
- Teach blackbody radiation and quantum physics
Scientific Background & Formulas
Wien’s displacement law: λ_max T = b, b = h c / (x k) ≈ 2897.77 µm·K where x ≈ 4.965114231 from transcendental solution of Planck’s law derivative.
Frequency form: ν_max = 5.879 × 10^10 T Hz
Applications: Sun λ_max ≈ 0.5 µm (green), human body ≈ 9.4 µm (LWIR), hot metal 1000 K ≈ 2.9 µm (NIR).
Validation: Exact match with NIST and astronomical observations.
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